Question

After simplifying the products in the given expression, which type of expression is obtained?

$2p(3p+4q)-5q(6p-7q)$

• A. Monomial
• B. Binomial
• C. Trinomial
• D. Polynomial

Answer 1

The correct option is C Trinomial

We are given with an algebraic expression $2p(3p+4q)-5q(6p-7q)$

$\underset{–}{Step1:}$

Simplifying the first product in the expression $2p(3p+4q)-5q(6p-7q)$

$2p(3p+4q)=(2p\times 3p)+(2p\times 4q)$

$=6p^{1+1}+8pq$ $(\because a^m\times a^n=a^{m+n})$

$=6p^2+8pq$

The product $2p(3p+4q)$ is equal to $6p^2+8pq$.

$\underset{–}{Step2:}$

Simplifying the second term in the product $2p(3p+4q)-5q(6p-7q)$

$5q(6p-7q)=(5q\times 6p)-(5q\times 7q)$

$=30qp-35q^{1+1}$ $(\because a^m\times a^n=a^{m+n})$
$=30qp-35q^2$
$=30pq-35q^2$ $(\because$ multiplication is commutative, i.e., $p\times q=q\times p)$

The product $5q(6p-7q)$ is equal to $30pq-35q^2$

$\underset{–}{Step3:}$

Now, putting the first and second terms in the product:
$2p(3p+4q)-5q(6p-7q)$
$=(6p^2+8pq)-(30pq-35q^2)$
$=6p^2+8pq-30pq+35q^2$

$=6p^2+\underset{–}{8pq-30pq}+35q^2$ (Since $8pq$ and $-30pq$ are like terms.)

$=6p^2-22pq+35q^2$

The product $2p(3p+4q)-5q(6p-7q)$ is equal to $6p^2-22pq+35q^2$.

As the simplified form of the product contains $3$ terms in it, it is a $\underset{–}{\text{trinomial}}.$

Therefore, option (c.) is the correct answer.